Download Frequency Modulation-Digital Signal Processing-Lab Manual and more Exercises Digital Signal Processing in PDF only on Docsity! University of Rhode Island Department of Electrical and Computer Engineering ELE 436: Communication Systems Experiment 5: Frequency Modulation 1 Introduction Angle modulation includes both phase modulation (PM) and frequency modulation (FM). The main difference between angle modulation and amplitude modulation is that in angle modulation, the information is contained in the angle of the carrier whereas in amplitude modulation, the information is in the amplitude of the carrier. We will be dealing only with FM in this lab. The theories and concepts are similar for PM. Why should we use FM instead of AM? The main advantages of using FM over AM are: 1. A Much better signal-to-noise ratio. There is as much as a 25-dB increase in this ratio over AM. You can notice this while listening to the car radio during a thunder storm. 2. When two FM transmitters are nearby operating on the same frequency, there is a much smaller geographical interference area as compared to AM transmitters operating on one frequency. 3. Less radiated power required for the same signal-to-noise ratio for FM over AM. There are also some serious disadvantages of FM. An FM wave typically requires 15 to 20 times the bandwith of an AM wave. Also, FM systems are much more complicated to analyze and build than AM systems. 2 FM theory At URI we have a radio station, 90.3 FM (WRIU). WRIU is a frequency modulated radio station with a carrier of 90.3MHz. Each FM station occupies a bandwidth of about 150kHz to 175kHz, but is alloted a bandwidth of about 200kHz; this is why each station is separated by 0.2 (MHz) on your dial. Let’s take a look at the modulation process to get a feel for what happens. The formula for an FM signal, s(t), is given by s(t) = Ac cos 2πfct+ 2πkf t ∫ 0 m(τ)dτ (1) 1 where m(t) = modulating signal fc = carrier frequency Ac = carrier amplitude Equation (1) is a general equation for an FM signal. If we let the modulating signal be a pure sinusoid, m(t) = Am cos2πfmt, then equation (1) becomes s(t) = Ac cos ( 2πfct+ kfAm fm sin 2πfmt ) = Ac cos (2πfct+ β sin 2πfmt) (2) where kfAm = ∆f = frequency deviation β = Modulation index There are two types of FM depending on the value of β. NBFM (β ¿ 1) If β is much less then 1, we have Narrow Band Frequency Modulation (NBFM). Equation (2) can be approximated as s(t) = Ac cos (2πfct)− βAc sin(2πfct) sin(2πfmt) (3) See the textbook and the class notes for details. WBFM (all β) The Wide Band Frequency Modulation formula is valid for all β. In this lab, we will be dealing with WBFM. The approximations used for NBFM are not accurate here. Using Fourier series coefficients, Equation (2) for WBFM can be written as (see text) s(t) = Ac ∞ ∑ n=−∞ Jn(β)cos [2π(fc + nfm)t] (4) where Jn(β) is the nth order Bessel function of the first kind and argument β. The definition of the Bessel function is shown below. It is an integral that needs to be evaluated using a calculator or software for different values of n and β. Jn(β) = 1 2π π ∫ −π ej(βsinx−nx)dx (5) Again, for details, see the text. 2
